This invention relates generally to positioning systems using signals broadcast from a plurality of orbiting satellites and, more particularly, to satellite-based differential positioning systems that determine the position coordinates of one receiver, referred to as a remote receiver, relative to the known position of another, referred to as the reference receiver.
There are two types of applications in which measurements of this kind may be usefully employed. One is referred to as kinematic positioning, in which the remote receiver may be moved with respect to the reference receiver, and the distance between the remote receiver and reference receiver is, therefore, not initially known. The other application is attitude determination, in which the distance between the remote and reference receivers is fixed, and the position of the remote receiver is used to determine the angular position of a line or chord joining the two receiver antennas. If three antennas are used instead of two, the angular position of a plane intersecting the three antennas can be determined from the relative positions of two of the antennas with respect to the third, used as a reference. Attitude determination has application in navigation systems on or above the earth. Using a platform having three antennas, the roll, pitch and yaw angles of a platform supporting the three antennas can be determined.
Satellite-based positioning systems, such as the Global Positioning System (GPS), provide a now widely used means for accurately determining the position of a receiver in three-dimensional space. These systems have numerous practical applications and, depending on the time duration over which measurements are taken, they can determine a receiver's position to sub-centimeter accuracy.
In GPS, a number of satellites orbiting the earth in well-defined polar orbits continually broadcast signals indicating their precise orbital positions. Each satellite broadcasts two modulated carrier signals, designated L.sub.1 and L.sub.2. The same two frequencies are used in transmitting from all of the satellites, but the satellites have unique pseudorandom digital codes that are used to modulate the L.sub.1 and L.sub.2 carriers. Each satellite signal is based on a precision internal clock, and the multiple clocks are effectively synchronized by ground-based stations that are a necessary part of GPS. The receivers detect superimposed modulated L.sub.1 and L.sub.2 signals and measure either or both of the code and carrier phase of each detected signal, relative to their own internal clocks. Even though a receiver clock is not synchronized with the satellite clocks, a receiver can nevertheless determine the "pseudorange" to each satellite based on the relative time of arrival of the signals, and the receiver position can then be mathematically determined from the pseudoranges and the known positions of the satellites. The clock error between the receiver's time reference and the satellite clocks can be eliminated by the availability of signals from an additional satellite. Thus, to solve for three unknown positional coordinates and the clock error requires the acquisition of four satellite signals.
GPS satellites provide two types of signals that can be used for positioning. The pseudorandom digital codes, referred to as the C/A code and the P code, provide unambiguous range measurements to each satellite, but they each have a relatively long "wavelength," of about 300 meters and 30 meters, respectively. Consequently, use of the C/A code and the P code yield position data only at a relatively coarse level of resolution. The other type of signal that can be used for position determination is the carrier signals themselves. The L.sub.1 and L.sub.2 carrier signals have wavelengths of about 19 and 24 centimeters, respectively. In a known technique of range measurement, the phase of one of the carrier signals is detected, permitting range measurement to an accuracy of less than a centimeter. The principal difficulty with using carrier signals for range measurement is that there is an inherent ambiguity that arises because each cycle of the carrier signal looks exactly alike. Therefore, the range measurement has an ambiguity equivalent to an integral number of carrier signal wavelengths. Various techniques are used to resolve the ambiguity. In a sense, the present invention is concerned with a novel technique for this type of ambiguity resolution.
In absolute positioning systems, i.e. systems that determine a receiver's position coordinates without reference to a nearby reference receiver, the process of position determination is subject to errors from a number of sources. These include orbital and ionospheric and tropospheric refraction errors. For attitude determination applications, the receivers are located so close together that these errors are completely negligible, that is to say they affect both or all three receivers substantially equally. For greater receiver spacings, as in kinematic positioning applications, such errors become significant and must be eliminated. It will be appreciated that the problems of attitude determination and kinematic positioning are closely analogous. The significant difference is that, in attitude determination, the distance between receivers is constrained. As a result, the receivers can be operated from a single reference clock. In a general sense, however, the attitude determination application is simply a more restricted form of the kinematic positioning problem.
In many kinematic positioning applications, a reference receiver located at a reference site having known coordinates is available for receiving the satellite signals simultaneously with the receipt of signals by the remote receiver. Depending on the separation distance, many of the errors mentioned above will be of about the same magnitude and will affect the various satellite signals they receive substantially equally for the two receivers. In this circumstance, the signals received simultaneously by two receivers can be suitably combined to substantially eliminate the error-producing effects of the ionosphere, and thus provide an accurate determination of the remote receiver's coordinates relative to the reference receiver's coordinates.
To properly combine the signals received simultaneously by the reference receiver and the remote receiver, and thereby eliminate the error-producing effects, it is necessary to provide an accurate initial estimate of the remote receiver's coordinates relative to the reference receiver. By far the easiest way to obtain the initial relative position of the remote receiver is to locate it at a pre-surveyed marker. Unfortunately, such markers are seldom available in many practical applications.
Another method often used to obtain an accurate initial relative position is to exchange the receivers and antennas between the reference and remote sites while both continue to operate. This results in an apparent movement between the two antennas of twice the vector difference between them. This apparent movement can be halved and used as the initial offset between them. The approach works well as long as the remote receiver is in the immediate vicinity of the reference site. Unfortunately, any time the satellite signals are lost the initial position must be reestablished, which means that the remote receiver must be returned to the control site or to a nearby marker. This is impractical in many applications, such as photogrammetric survey by aircraft.
In a prior patent to Ronald R. Hatch, U.S. Pat. No. 4,812,991, a method using carrier smoothed code measurements to determine an increasingly accurate initial position was described. This technique had the advantage that it did not require the remote receiver to remain stationary while the initial relative position was established. The disadvantage of that method is twofold. First, it is not an instantaneous method of establishing the initial position and can take several minutes of data collection and processing to accomplish the task. Second it requires access to the the precise (P) code modulation on the L.sub.2 carrier frequency. Unfortunately, the United States Department of Defense has reserved the right to limit access to P code modulation by encrypting the P code prior to transmission from each satellite. Therefore, the method described in the prior patent cannot be used when access to the P code is denied.
It will be appreciated from the foregoing that there is a significant need for a new approach to the determination of the position of a remote receiver, which may be moving, with respect to a reference receiver, both for kinematic positioning systems and for attitude determination systems. Ideally, the new technique should not be subject to the disadvantages of the prior art, i.e. it should not require access to the P code modulating signal, it should not constrain motion of the remote receiver, and it should operate on a practically instantaneous basis. The present invention fulfills this need.